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Rahmat Hidayat
Makassar State University
Mathematics

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A Systematic Simulation Study of Semiparametric Spline Estimators for Nonlinear Data Structures in R Rahmat Hidayat; Aswi Aswi; Zakiyah Mar'ah
Journal of Mathematics, Computations and Statistics Vol. 9 No. 2 (2026): Volume 09 Issue 02 (June 2026)
Publisher : Jurusan Matematika FMIPA UNM

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35580/7k3vqe29

Abstract

In many real-world applications, the assumption of linearity in classical regression models is often violated, leading to model misspecification and inaccurate estimation when data exhibit complex nonlinear patterns. Although nonparametric approaches provide flexibility, they frequently suffer from poor interpretability and instability in high-dimensional settings. To address these limitations, this study examines the implementation of semiparametric spline regression as a flexible yet interpretable alternative. The model integrates a linear component for certain predictors and a spline-based nonparametric component to capture local data fluctuations. Through a simulation study using the R programming language, the performance of the spline estimator was evaluated based on the Generalized Cross Validation (GCV) criterion for optimal knot selection. The results demonstrate that the semiparametric spline model achieves superior accuracy, with a coefficient of determination (R²) reaching 97.35%, compared to 81.18% for the classical linear model. In addition, the Mean Square Error (MSE) is significantly reduced from 2.158 to 0.303. Residual diagnostic analysis confirms that the model satisfies normality and homoscedasticity assumptions. These findings highlight the effectiveness of spline-based semiparametric regression in modeling complex nonlinear data structures.
Co-Authors Aswi, Aswi Zakiyah Mar'ah